Observing emergent hydrodynamics in a long-range quantum magnet

TL;DR

This paper experimentally demonstrates the emergence of various hydrodynamic behaviors, including normal and anomalous diffusion, in a long-range interacting quantum spin chain of ions, revealing universal non-equilibrium properties.

Contribution

It provides the first experimental observation of multiple hydrodynamic universality classes in a controlled quantum system with long-range interactions.

Findings

Observation of normal diffusion and superdiffusion in a quantum spin chain

Measurement of transport coefficients reflecting microscopic interactions

Identification of Lévý flight dynamics in quantum hydrodynamics

Abstract

Identifying universal properties of non-equilibrium quantum states is a major challenge in modern physics. A fascinating prediction is that classical hydrodynamics emerges universally in the evolution of any interacting quantum system. Here, we experimentally probe the quantum dynamics of 51 individually controlled ions, realizing a long-range interacting spin chain. By measuring space-time resolved correlation functions in an infinite temperature state, we observe a whole family of hydrodynamic universality classes, ranging from normal diffusion to anomalous superdiffusion, that are described by L\'evy flights. We extract the transport coefficients of the hydrodynamic theory, reflecting the microscopic properties of the system. Our observations demonstrate the potential for engineered quantum systems to provide key insights into universal properties of non-equilibrium states of quantum matter.